# [R-sig-ME] parameter restrictions

dave fournier davef at otter-rsch.com
Tue Oct 18 02:20:14 CEST 2011

```I don't think it is very difficult. Something like this should do the job.
It depends on how you want to model the correlation of the random effects.
Perhaps the ADMB list would be the place to discuss it.

DATA_SECTION
int nfixed
!! nfixed=7;  // for this example
init_int nobs   // number of observations
init_int nrand   // number of observations
init_vector Y(1,nobs)   // observations
init_matrix X(1,nobs,1,nfixed)  // fixed effects design matrix
init_matrix Z(1,nobs,1,nrand)   // random effects design matrix
PARAMETER_SECTION
init_number a
init_bounded_vector alpha(2,nfixed,0.0,1.0)
objective_function_value f
!! int nr1=nrand*(nrand-1)/2; // number of parameters needed for
correlation
init_vector c(1,nr1)   // parameters for choleski decomp
// of the correlation matrix
init_vector log_sigma(1,nrand)           // log of variances
random_effects_vector u(1,nrand)
PROCEDURE_SECTION
// parameterize the b's to satisfy constraints
dvar_vector b(1,nfixed);
b(1)=-exp(a);
dvariable ssum=0.0;
for (int i=2;i<=nfixed;i++) {
ssum-=b(i-1);
b(i)=alpha(i)*ssum;
}
// choleski decomp of correlation matrix
dvar_matrix C(1,nrand,1,nrand);
C.initialize();
int ioffset=1;
for (int i=1;i<=nrand;i++) {
C(i,i)=1;
if (i>1)
{
C(i)(1,i-1)=c(ioffset,ioffset+i-1).shift(1);
C(i)/=norm(C(i));
ioffset+=i-1;
}
C(i)*=exp(log_sigma(i));   // turn it into Choleski decomp of
covariance
// matrix
}
dvar_vector v=C*u;           // now v has right covariance
dvar_vector pred_Y=X*b+Z*v;  // predicted Y
dvar_vector r=Y-pred_Y;
dvariable w=norm2(r)/nobs;   // mean square error
f=0.5*nobs*log(w);    // concemntrated likelihood
f+=0.5*norm2(u);    // log prior  for u

```